Superconvergence analysis for nonlinear Schrödinger equation with two-grid finite element method

DOI10.1016/J.AML.2021.107553OpenAlexW3184546095MaRDI QIDQ2236730

Meng Li, Lijuan Guo, Junjun Wang

Publication date: 26 October 2021

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2021.107553

zbMATH Keywords

nonlinear Schrödinger equationtwo-grid finite element methodsuperconvergence analysisunconditional results

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) NLS equations (nonlinear Schrödinger equations) (35Q55) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

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Cites Work

• Unnamed Item
• A new error analysis of Crank-Nicolson Galerkin FEMs for a generalized nonlinear Schrödinger equation
• A compact split-step finite difference method for solving the nonlinear Schrödinger equations with constant and variable coefficients
• Two-grid method for two-dimensional nonlinear Schrödinger equation by mixed finite element method
• Local discontinuous Galerkin methods for nonlinear Schrödinger equations
• Two-grid method for the two-dimensional time-dependent Schrödinger equation by the finite element method
• Conforming and nonconforming conservative virtual element methods for nonlinear Schrödinger equation: a unified framework
• Unconditional superconvergence analysis of a Crank-Nicolson Galerkin FEM for nonlinear Schrödinger equation
• Uniform Error Estimates of Finite Difference Methods for the Nonlinear Schrödinger Equation with Wave Operator
• Finite difference discretization of the cubic Schrödinger equation
• A Space-Time Finite Element Method for the Nonlinear Schrödinger Equation: The Continuous Galerkin Method
• A space-time finite element method for the nonlinear Schrödinger equation: the discontinuous Galerkin method
• Uniform and Optimal Error Estimates of an Exponential Wave Integrator Sine Pseudospectral Method for the Nonlinear Schrödinger Equation with Wave Operator

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